ON some analytical index formulas related to operator-valued symbols

Electronic Journal of Differential Equations

Volumn 2002, Issue , 2002, Pages

  Rozenblum, Grigori ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Cyclic cohomology; Index; Pseudodifferential operators; Singular manifolds

Indexed keywords

EID: 52449118016     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. B. Blackadar, K-theory for Operator Algebras, Springer, NY, 1986.
2. A. Connes, Noncommutative Differential geometry, Publ. Math. I.H.E.S, Vol. 62, 1985, pp. 257-360.
3. A. Connes, Noncommutative Geometry, Academic Press, NY, 1994.
4. C. Dorschfeldt, Algebras of pseudodifferential operators near edge and corner singularities, Whiley-VCH Verlag, Berlin, 1998.
5. C.Dorschfeldt, B.-W. Schulze, Pseudo-differential operators with operator-valued symbols in the Mellin-edge-approach, Ann. Global Anal. Geom., Vol. 12, 1994, pp. 135-171.
6. B. Fedosov, Analytic formulas for the index of elliptic operators, Trans. Moscow Math. Soc., Vol. 30, 1974, pp. 159-240.
7. B. Fedosov, Analytic formulas for the index of an elliptic boundary value problem, Math. USSR Sbornik, Vol. 22, pp. 61-90, 1974. Vol. 24, pp. 511-535, 1974. Vol 30, pp. 341-359, 1976.
8. B. Fedosov, B.-W. Schulze, On the index of elliptic operators on a cone, Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras, pp. 348-372, Akademie Verlag, Berlin, 1996.
9. B.Fedosov, B.-W. Schulze, N. Tarkhanov, On the index of elliptic operators on a wedge, J. Funct. Anal., Vol. 157, 1998, pp. 164-209.
10. V. Guillemin, Gauged Lagrangian distributions, Adv. Math., Vol. 102, 1993, pp. 184-201.
11. L. Hörmander, On the index of pseudodifferential operators Elliptische Differentialgleichungen, Band II, Akademie-Verlag, pp. 127-146, 1969.
12. B. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., Vol. 127, 1972.
13. J.J. Kohn, L. Nirenberg, An algebra of pseudodifferential operators, Commun. Pure Appl. Math., Vol. 18, 1965, pp. 269-305.
14. M. Karoubi, Homologie cyclique et K-théorie, Astérisque, No 149, 1987.
15. G. Luke, Pseudodifferential operators on Hubert bundles, Journal Diff. Equat., Vol. 12, pp. 566-589, 1972.
16. R. Melrose, The eta invariant and families of pseudodifferential operators, Math. Res. Lett., Vol. 2, 1995, pp. 541-561.
17. R. Melrose, Fibrations, compactifications and algebras of pseudodifferential operators, Partial Diff. Equations and Math. Physics. The Danish-Swedish Analysis Seminar, Birkhäuser, 1996, pp. 246-261.
18. R. Melrose, P. Piazza, Analytic K-theory for manifolds with corners, Advances Math., Vol. 92, 1992, pp. 1-27.
19. B. Plamenevsky, Algebras of pseudodifferential operators Mathematics and its Applications (Soviet Series), 43, Kluwer Academic Publishers Group, Dordrecht, 1989.
20. B. Plamenevsky, G. Rozenblum, On the index of pseudodifferential operators with isolated singularities in the symbols (Russian), Algebra i Analiz, Vol. 2, 1990, No. 5, pp. 165-188. Translation in Leningrad Math. J., Vol. 2, 1991, 1085-1110.
21. B Plamenevsky, G. Rozenblum, Topological characteristics of the algebra of singular integral operators on the circle with discontinuous symbols (Russian), Algebra i Analiz, Vol. 3 (5), 1991, pp. 155-167. Translation in St. Petersburg Math. J., Vol. 3, 1992.
22. B. Plamenevsky, G. Rozenblum, Pseudodifferential operators with discontinuous symbols: K-theory and index formulas (Russian), Funktsional. Anal, i Prilozhen., Vol. 26, 1992 No. 4, pp. 45-56. Translation in Functional Anal. Appl., Vol. 26, 1993, pp. 266-275.
23. B. Plamenevsky, V. Senichkin, Representations of an algebra of pseudodifferential operators with multidimensional discontinuities in the symbols (Russian), Izv. Akad. Nauk SSSR Ser. Mat., Vol. 51, 1987, pp. 833-859. Translation in Math. USSR-Izv. Vol. 31, 1988, pp. 143-169.
24. B.Plamenevsky, V. Senichkin, Solvable operator algebras, St. Petersburg Math. J., Vol. 6, 1995, pp. 895-968.
25. B. Plamenevsky, G. Tashchiyan, A convolution operator in weighted spaces (Russian), Nonlinear equations and variational inequalities. Linear operators and spectral theory, pp. 208-237, 1990. Probl. Mat. Anal., 11, Leningrad. Univ. Leningrad.
26. G. Rozenblum, On a class of pseudodifferential operators with operator-valued symbols, Preprint Linköping University, 1992.
27. G. Rozenblum, Index formulae for pseudodifferential operators with discontinuous symbols, Ann. Global Anal. Geom., Vol. 15, 1997, pp. 71-100.
28. G. Rozenblum, The index of cone M ellin operators, Geometric aspects of partial differential equations (Roskilde, 1998), 1999 pp. 43-49, Contemp. Math., 242, Amer. Math. Soc., Providence, RI.
29. E. Schrohe, Fréchet Algebras of Pseudodifferential Operators and Boundary Problems, 2000, Birkhäuser, Basel.
30. E. Schrohe, A short introduction to Boutet de Monvel's calculus, Preprint 2000/03, Univ. of Potsdam, 2000.
31. E. Schrohe, J. Seiler, An analytic index formula for pseudodifferential operators on wedges, Preprint, Max-Planck-Institut fur Mathematik, 96-172, 1996.
32. B.-W. Schulze, Pseudodifferential operators on manifolds with singularities, 1991, North Holland, Amsterdam.
33. B.-W. Schulze, Pseudo-differential Boundary Value Problems, Conical Singularities, and Asymptotics, 1994, Académie-Verlag, Berlin.
34. B.-W. Schulze, Boundary Value Problems and Singular Pseudodifferential Operators, J. Whiley, Chichester, 1998.
35. B.-W. Schulze, Operator algebras with symbol hierarchies on manifolds with singularities, Preprint 99/30, Universitet Potsdam, 1999.
36. B.-W. Schulze, B. Sternin, V. Shatalov, Differential Equations on Singular Manifolds: Semiclassical Theory and Operator Algebra, 1999, Wiley, Weinheim.
37. B.-W. Schulze, B. Sternin, V. Shatalov, On the index of differential operators on manifolds with conical singularities, Ann. Global Anal. Geom., Vol. 16, 1998, pp. 141-172.
38. B.-W Schulze, N. Tarkhanov, Pseudodifferential operators on manifolds with corners, preprint 2000/13, Univ. of Potsdam, 2000.
39. V. Senichkin, Pseudodifferential operators on manifolds with edges, J. Math. Sei., Vol. 73, 1995, pp. 711-747.